A line with positive direction cosines passes through the point $P(2,-1,2)$ and makes equal angle with coordinate axes. The line meets the plane $2x+y+z=9$ at the point $Q$. The length of the segment $PQ$=?

Question

$\begin{array}{1 1} 1 \\ \sqrt 2 \\ \sqrt 3 \\ 2 \end{array}$